Efficient Algorithms for the Implementation of General B-Splines

Ferrari, Leonard A.; Silbermann, Martine J.; Sankar, P. V.

doi:10.1006/cgip.1994.1009

Cited by 3 publications

(4 citation statements)

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“…We cat1 this the direct approach to the computation of Q"'(U). As shown in [9], this is not the most efficient procedure.…”

Section: A Efficient Implementation Of Spline Curves As Stated By Ementioning

confidence: 99%

“…Fewer variables not only save in the computational complexity of rendering but also simplifying other computations used frequently in graphics applications (e.g., linear transformations). In [9], the relationship between the r-th derivative of an r-th-order B-spline and the (r -1)-th derivative of two other (r -1)-th-order B-splines was developed. We repeat the result here as shown in Eq.…”

Section: The Derivative/summation Algorithmmentioning

confidence: 99%

“…We repeat the result here as shown in Eq. (9). In [ l l ] , a set of recurrence equations for both simple knot and multiple knot cases was derived.…”

Section: The Derivative/summation Algorithmmentioning

confidence: 99%

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High-speed computation of spline functions and applications

Wang

Ferrari

Silbermann

1996

Int. J. Imaging Syst. Technol.

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“…We cat1 this the direct approach to the computation of Q"'(U). As shown in [9], this is not the most efficient procedure.…”

Section: A Efficient Implementation Of Spline Curves As Stated By Ementioning

confidence: 99%

Section: The Derivative/summation Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

High-speed computation of spline functions and applications

Wang

Ferrari

Silbermann

1996

Int. J. Imaging Syst. Technol.

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“…Various papers [5,13,15] give rapid algorithms for the computation of the derivatives of an arbitrary order BSpline, and demonstrate that knot refinement algorithms based on the above observation are an order of magnitude faster than the well-known Oslo algorithm [2].…”

Section: Introductionmentioning

confidence: 99%

Efficient Degree Elevation and Knot Insertion for B-spline Curves using Derivatives

Huang¹,

Hu²,

Martin³

2004

Computer-Aided Design and Applications

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This paper presents a new algorithm for raising the degree of a B-spline curve which can also insert new knots at the same time. The new algorithm is faster than existing algorithms, and is much easier to understand and to implement. The new control points are computed using the following three simple steps: computing derivatives from control points, resampling the knot vector, and computing new control points from derivatives. Comparisons with previous methods and examples are given.

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Automatic Data Visulization Using Spline Functions

Wang¹,

Ferrari²

1990 Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers, 1990.

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This paper presents an algorithm for automatically approximating arbitrary curves using B-spline functions. Both knot locations and control vertices are treated as variables. This makes the approximation problem nonlincar. The algorithm which is proposed basically adapts steepest descent concepts to aid the graphics designer in searching the knots and control vertices automatically. A "knot insertion" method is also used to decrease the cost function.

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Efficient Algorithms for the Implementation of General B-Splines

Cited by 3 publications

References 0 publications

High-speed computation of spline functions and applications

High-speed computation of spline functions and applications

Efficient Degree Elevation and Knot Insertion for B-spline Curves using Derivatives

Automatic Data Visulization Using Spline Functions

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